- Email: [email protected]
Energetics of LCST transition of poly(ethylene oxide) in aqueous solutions
Polymer 73 (2015) 86e90
Contents lists available at ScienceDirect
Polymer journal homepage: www.elsevier.com/locate/polymer
Energetics of LCST transition of poly(ethylene oxide) in aqueous solutions Valerij Y. Grinberg a, *, Tatiana V. Burova a, Natalia V. Grinberg a, Alexander S. Dubovik b, Vladimir S. Papkov a, Alexei R. Khokhlov a a b
A.N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Vavilov St. 28, 119991 Moscow, Russian Federation N.M. Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, Kosygin St. 4, 119991 Moscow, Russian Federation
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 April 2015 Received in revised form 22 June 2015 Accepted 20 July 2015 Available online 22 July 2015
Poly(ethylene oxide), PEO, is known to undergo a phase separation transition in aqueous solutions upon heating. This LCST transition is first investigated by high-sensitivity differential scanning calorimetry. Dependences of the transition temperature (Tt), enthalpy (Dth) and heat capacity increment (Dtcp) on the polymer concentration are determined. The transition temperature and enthalpy of PEO decreased with increasing the polymer concentration and followed the Kirchhoff law. A substantial positive value of the transition heat capacity increment of PEO is detected suggesting that the transition is accompanied by an exposure of the polymer hydrophobic groups to water. Comparison of Dtcp with the corresponding change in the accessible surface area of PEO reveals that the LCST transition of PEO may involve cooperative conformational changes of the type of helixecoil transition in PEO macromolecules. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Poly(ethylene oxide) LSCT DSC
1. Introduction Poly(ethylene oxide), PEO, is known as one of the most important water-soluble polymers that has wide practical application [1]. PEO is unlimitedly soluble in water at normal conditions. However, solubility of PEO decreases upon heating, and its aqueous solutions undergo phase separation at a high enough temperature. LCST of aqueous solutions of PEO varies from 100 to 180 C depending on the polymer molecular weight [2,3]. Most of the theories of the phase separation of aqueous PEO solutions [4e6] consider macromolecules of PEO as flexible chains. At the same time, numerous indirect data are available suggesting that macromolecules of PEO in aqueous solution have a helical structure under normal conditions [7e12]. This feature is taken into account in the theory of the LCST behavior of PEO proposed by €m [8]. According to this theory, stability of the helical Karlstro conformation of PEO should depend on temperature. The helix is stable at rather low temperatures, while at elevated temperatures PEO undergoes conformational changes of the type of helixecoil transition. This very transition induces phase separation of the aqueous PEO solutions upon heating. This interesting concept has
* Corresponding author. E-mail address: [email protected] (V.Y. Grinberg). http://dx.doi.org/10.1016/j.polymer.2015.07.032 0032-3861/© 2015 Elsevier Ltd. All rights reserved.
not found a reliable experimental support until now. In this paper we report an experimental evidence of a helixecoil transition of PEO in aqueous solutions associated with the phase separation of these solutions upon heating. The data were obtained by highsensitivity differential scanning calorimetry (HS-DSC) [13]. Besides temperature and enthalpy of the phase separation these data include estimations of change in the partial heat capacity of the polymer related to the phase separation, i.e. the transition heat capacity increment, Dtcp. This parameter correlates with changes in the accessible surface area of a macromolecule (ASA) [14e16]. According to our data the transition heat capacity increment of PEO is positive. This suggests that PEO macromolecules in the initial state (low temperatures) have a hydrophobic interior. One of the probable structures possessing hydrophobic interior might be a helix. Therefore the phase separation of the PEO solutions may be coupled with a conformational helixecoil transition of this polymer. 2. Experimental Poly(ethylene oxide) of a molecular weight of Mh ¼ (43 ± 2) 103 was purchased from Merck and used without additional purification. Aqueous salt-free solutions of this polymer of rather low concentrations revealed phase separation at temperatures 110e130 С. In this temperature range it is not possible to
V.Y. Grinberg et al. / Polymer 73 (2015) 86e90
perform precise calorimetric measurements of the polymer partial heat capacity in an aqueous medium. The most appropriate temperature interval for such measurements is 20e80 С. For this reason we had to reduce the transition temperature of the PEO phase separation to the optimal value (~40 C), lying in the middle of this range. The decrease in the phase separation temperature means a decrease in solvent quality with respect to the polymer. One of the most evident manifestation of the worsening of solvent quality is a decrease in the q-temperature. Boucher and Hines [17] determined values of the q-temperature of PEO in aqueous solutions of various lyotropic salts. They found that the lyotropic salts reduce the q-temperature of PEO. This effect correlates with the salt position in the Hofmeister series. The most distinct changes were observed in case of carbonates and sulfates. Sulfates, being highly thermostable, looked more appropriate for the DSC experiments. The q-temperature of PEO decreases to 41 С at the concentration of ammonium sulfate of 0.5 mol L1. For this reason we have chosen 0.5 М (NH4)2SO4 as a solvent. The PEO concentration was varied from 4 to 75 mg mL1. Calorimetric measurements were carried out with a differential adiabatic scanning microcalorimeter DASM-4 (“Biopribor”, Pushchino, Russia) within the temperature interval 20e70 C at a heating rate of 1.0 K min1. The conversion of raw data to the temperature dependences of the partial heat capacity of the polymer was performed by a standard method [13] using the tabulated values of density and heat capacity of 0.5 M (NH4)2SO4 [18] and the partial specific volume of PEO (v ¼ 0.838 cm3 g1) [19]. The conversion of the temperature dependences of the partial heat capacity to the excess heat capacity functions was carried out by the Takahashi-Sturtevant method [20]. The transition temperature Tt was determined as a temperature that corresponds to the maximum of the excess heat capacity curve, and the transition enthalpy Dth e as an area under this curve. The transition heat capacity increment Dtcp was determined by a counter extrapolation of the linear segments of the partial heat capacity function before and after the transition to the transition temperature. All calculations were performed with the use of a proprietary software NAIRTA 2 (Institute of Biochemical Physics, Moscow) based on the standard algorithms of HS-DSC data processing [13]. The cloud point temperatures Tcp of the PEO solutions of different concentrations were visually determined with an accuracy of ±0.25 С during heating with a constant rate of 1.0 K min1.
87
to determine only the transition temperature because of experimental limitations (a small instrument response at low polymer concentrations and an uncompensated imbalance of the calorimetric cells at high ones). The concentration dependences of the calorimetric transition parameters (Tt, Dth, Dtcp) and of the cloud points are given in Fig. 2. One can see that the calorimetric transition temperatures coincide well with the cloud point temperatures. In the concentration range 18e50 mg mL1, where the precise determination of all calorimetric parameters was possible, the transition temperature and enthalpy decrease from 56.4 to 48.9 С and from 4.2 to 2.4 J g1, respectively, while the transition heat capacity increment remains practically unchanged (Dtcp ¼ 0.31 ± 0.04 J g1 К1). Additionally, for more consistent determination of Dtcp we used the approach based on correlation between the transition enthalpy and temperature [21]. The enthalpy of the PEO phase transition is plotted against the transition temperature in Fig. 3. We observe a good linear correlation between values of these parameters. The correlation implies that heat effects, which are not related to the transition, do not contribute to the calorimetric enthalpy. In this case the calorimetric parameters satisfy the Kirchhoff law [22], which assigns the slope of the linear dependence Dth(Tt) to the transition heat capacity increment Dtcp. Applying the Kirchhoff law to the data in Fig. 3, we determine Dtcp ¼ 0.22 ± 0.02 J g1 К1. This is close to the result of the direct calorimetric determination of the transition heat capacity increment, as described above (Dtcp ¼ 0.31 ± 0.04 J g1 К1). The agreement of the direct and indirect determinations of the heat capacity increment suggests the thermodynamic consistency of the average value of this parameter Dtcp ¼ 0.27 ± 0.05 J g1 К1. It is necessary to emphasize that this parameter is positive and similar by the magnitude to unfolding heat capacity increments of proteins [23]. It is well recognized that the positive heat capacity increment of protein unfolding is a clear manifestation of existence of hydrophobic core in protein molecule [24]. Here we come to two important differences between PEO and the most studied thermoresponsive polymers, poly(Nisopropylacrylamide) (PNIPAM) and poly(N-vinylcaprolactam) (PVCL). For these two polymers the enthalpy of LCST transition is of about 60 J g1 and the transition heat capacity increment is negative (~0.6 J g1 K1) [25,26].
3. Results and discussion Fig. 1 shows an example of the temperature dependence of the partial heat capacity of PEO in aqueous solution at the polymer concentration of 22.5 mg mL1. The partial heat capacity increases linearly with increasing temperature within the interval from 20 to 50 C, then passes though a sharp maximum and reaches a constant level notably exceeding the partial heat capacity of the polymer in the pre-transition area. The temperature of the partial heat capacity maximum coincides with the cloud point temperature of the PEO solution. This allows us to assign the observed changes in heat capacity in the post-transition area to the phase separation of the system. It is important that the phase separation of the PEO aqueous solutions is accompanied by an increase in the polymer partial heat capacity (Dtcp > 0) along with a trivial heat absorbance (Dth > 0). Similar temperature dependences of the partial heat capacity of PEO were determined at different polymer concentrations from 4 to 75 mg mL1. However, their complete quantitative analysis (that is, determination of all calorimetric parameters: Tt, Dth and Dtcp) was only possible within the more narrow interval from 18 to 50 mg mL1. At the lower and higher concentrations we were able
Fig. 1. Partial heat capacity of PEO in aqueous solution (polymer concentration 22.5 mg mL1, 0.5 M (NH4)2SO4). The thin and dash lines represent a transition base line and a linear approximation of the pre-transition segment of the partial heat capacity function, respectively.
88
V.Y. Grinberg et al. / Polymer 73 (2015) 86e90
It is possible to relate the difference in the transition enthalpies of PEO and the poly(N-alkylamides) with differences in hydration mechanisms of these types of polymers. The hydration mechanism of PEO is associated with binding of water molecules to independent identical sites on the polymer matrix [4]. On the contrary, the poly(N-alkylamides) hydration seems to be very cooperative [27]. Heat effects of phase separation of aqueous solutions of thermoresponsive polymers is commonly attributed to their dehydration [28]. The non-cooperative hydration mechanism assumes that the dehydration constitutes dissociation of bonds between water molecules and the polymer matrix. On the other hand, in the case of the cooperative mechanism the dehydration should additionally include breakdown of bonds between water molecules bound to neighboring sites on the polymer matrix. That is why the transition enthalpy of the poly(N-alkylamides) greatly exceeds the transition
enthalpy of PEO. The phase separation of aqueous solutions of the poly(Nalkylamides) is accompanied by a decrease in the partial heat capacity of the polymer (Dtcp < 0) [25,26]. It is due to the fact that some links of the polymer chain, initially accessible to water molecules, become inaccessible to them after the phase transition. This indicates existence of a hydrophobic core in the concentrated polymer phase formed as a result of the phase separation. A positive value of the transition heat capacity increment of PEO suggests that some part of hydrophobic fragments of PEO macromolecule in its initial conformation at low temperatures is inaccessible to water molecules [14,16]. The question arises what structure of PEO may have a hydrophobic interior? The chain stereochemistry of PEO allows the formation of helical conformation [29]. This conformation is experimentally observed in the crystal state of the polymer [30]. The data on the probability of existence of PEO helixes in aqueous solution are rather contradictory. On the one hand, there are indirect experimental data [9e11,31e33] and certain model simulations [7,8,12] suggesting that molecules of PEO retain helical conformation in aqueous medium. On the other hand, the SANS data show that molecules of PEO in aqueous solution have the conformation of a random coil [34]. The reason for this contradiction is probably a high lability of the PEO conformation in aqueous solution. In order to shift the conformational equilibrium towards the helix it is necessary to increase its stability with respect to the coil conformation. This can be achieved in two ways e either by strengthening bonds between peripheral oxygen atoms, or by enhancing interaction of hydrophobic groups forming the helix interior. The first scenario was described in the works of Alessi et al. [34] and Norman et al. [35]. It has been shown by SANS that the helix is a preferential conformation of PEO in solutions of neat carboxylic acids with a number of carbon atoms from 3 to 5. The nature of such a phenomenon could be explained in the following manner. It is well known that oxygen atom of PEO can form H-bond with the protonated carboxylic group. This interaction determines the ability of PEO to form complexes with polymeric acids in the protonated state [36]. One can imagine that the carboxylic acids, being bound to the neighboring oxygen atoms on the helix surface, create bonds between the helix turns by means of van der Waals
Fig. 2. Transition temperature (a), enthalpy (b) and heat capacity increment (c) of PEO in aqueous solutions (0.5 M (NH4)2SO4) vs the polymer concentration: (1) e calorimetric data; (2) e cloud points (explanations in text).
Fig. 3. Correlation between the transition enthalpy and temperature for PEO in aqueous solutions (0.5 M (NH4)2SO4) of different polymer concentrations according to the Kirchhoff law. The slope of correlation line is 0.22 ± 0.02 J g1 K1.
V.Y. Grinberg et al. / Polymer 73 (2015) 86e90
interactions of their alkyl groups. The second scenario of the PEO helix stabilization implies the strengthening of hydrophobic interaction of the groups, forming interior of the helix. This situation seems to be relevant to the conditions used in our study. It is well known that lyotropic salts, such as ammonium sulfate, enhance hydrophobic interaction in aqueous medium [37] as evidenced by multiple effects, such as a decrease in the precipitation temperature of amphiphilic polymers [38] or an increase in conformational stability of globular proteins and helical peptides in solutions of lyotropic salts [39]. Thiyagarajan et al. [40] have shown by means of SANS that in solutions of sodium carbonate, which is a strong salting-out solute, PEO is represented by rod-like particles of the length proportional to the polymer molecular weight, determined in neat water. From these data it can be concluded that the length of such a particle per one polymer link is equal to 3.0 ± 0.1 Å. On the other hand, the results of molecular modeling [12] show that the helix length per one link is of about 2.9 Å. This coincidence may be considered as an indirect confirmation of the concept that PEO adopts the helical conformation in solutions of lyotropic salts. On this basis it is reasonable to suggest that under the conditions of our experiment, i.e. in 0.5 M solution of ammonium sulfate, the helical conformation of PEO is rather stable at temperatures below the phase separation temperature. Upon heating the helices melt, their hydrophobic interior breaks, the chain hydrophobic groups become exposed to the aqueous surrounding, their random association begins and causes the polymer precipitation. In certain aspects this resembles the denaturation behavior of globular proteins, which demonstrate similar disintegration of a molecular hydrophobic core upon heating that often leads to the precipitation of the denatured proteins [41,42]. It has been shown on the example of proteins that the transition heat capacity increment is closely related to the change in the accessible surface area (DtASA) of a macromolecule associated with the transition [15,16,24]. According to the data by Spolar et al. [15], hydration of apolar and polar groups is accompanied by the intrinsic changes in heat capacity. Values of these changes per unit of the accessible surface area equal to Dh CpAPO ¼ 1.338 J mol1 К1 Å2 and Dh CpPOL ¼e 0.585 J mol1 К1 Å2, respectively. The universality of these increments was shown for a great number of compounds. Taking into account this fact, we can assume that the heat capacity increment of the PEO transition is directly related to the change in the chain hydration as a result of the helix unwinding. If so, the specific heat capacity increment can be calculated as:
. M0 Dt cp ¼ Dh CpAPO Dt ASAAPO þ Dh CpPOL Dt ASAPOL
(1)
where DtASAAPO and DtASAPOL are the changes in the accessible area of the hydrophobic and hydrophilic surface of PEO monomer unit induced by the helixecoil transition, respectively; and M0 ¼ 44 g mol1 is the molecular weight of PEO monomer unit. According to the molecular modeling data [12], the PEO helix in water has the following characteristics: the helix pitch LH ¼ 16 Å; the diameter of the helix DH x 5 Å; the number of monomers per a helix turn nH ¼ 11/2. Accordingly, the area of the accessible surface of the helix per monomer is:
ASAH ¼
pLH DH nH
(2)
A value of the accessible surface area per monomer for PEO in the coil state can be determined by an additive scheme [14]:
ASAC ¼ 2ASACH2 þ ASAO
(3)
where ASACH2 and ASAO are the accessible surface areas of the CH2
89
group and an oxygen atom, respectively. The value ASACH2 may be also estimated by the additive scheme, using values of the accessible surface area of the leucine and valine residues [14] ASAILE ¼ 137 Å2 and ASAVAL ¼ 117 Å2: ASACH2 ¼ ASAILE ASAVAL . A value of the accessible surface area of the oxygen atom ASAO ¼ 50 Å2 is reported in the work by Petukhov et al. [43]. It is important that in the first approximation the distribution of the accessible area of the PEO monomer by hydropathy is the same for the coil and helix. It can be roughly estimated by the fractions of the hydrophobic and hydrophilic surfaces XAPO ¼ 2ASACH2 =ASAC ¼ 0:444 and XPOL ¼ ASAO/ASAC ¼ 0.556. Thus the transition change in hydrophobic and hydrophilic accessible surface area of PEO per monomer will be:
Dt ASAPOL ¼ XPOL ðASAC ASAH Þ
(4)
and
Dt ASAAPO ¼ XAPO ðASAC ASAH Þ
(5)
According to the calculations by Equations (1)e(5), the heat capacity increment of the helixecoil transition of PEO in aqueous solution is equal to 0.27 J g1 К1. This estimate coincides with the average value of the specific transition heat capacity increment of PEO determined directly from the HS-DSC data and by the Kirchhoff law (Dtcp ¼ 0.27 ± 0.05 J g1 К1) . Thus, the calorimetric data on energetics of the phase separation of aqueous solutions of PEO point to at least two particular features of behavior of this polymer in aqueous salt solution, which may be important for structural considerations. First, a relatively small enthalpy of the PEO phase transition (about of several Joule per gram of the polymer) reflects presumably a noncooperative mechanism of the polymer hydration. Second, the transition is accompanied by increase in the partial heat capacity of the polymer typical for protein unfolding when initially buried hydrophobic groups of the protein become accessible to water molecules. On this basis we could suggest that macromolecules of PEO in the pre-transition state assume a conformation with a defined hydrophobic core. Such a conformation could be helix, existence of which was shown to be consistent with numerous indirect experimental data and some results of molecular simulations. Upon heating the helix melts providing complete accessibility of PEO links to water molecules that provokes the phase separation.
4. Conclusion Despite a long-term representative history of investigation of PEO, its solution structure remains an open question. Many reliable facts indicate a clear tendency of PEO to form rod-like particles in aqueous solutions, particularly under salting-out conditions. Fine characterization of these structures is obviously complicated by their high lability and sensitivity to various polymer and environment parameters, such as salt nature and concentration, temperature, molecular characteristics of PEO, etc. The experimental and theoretical approaches that include consideration of the transition energetics may help to fill the structural gap, exploring phase and conformational transitions of these labile structures and analyzing contributions of certain interactions to the transition parameters. The first direct data on energetics of the phase separation of aqueous solutions of PEO support the existing hypothesis on the probability of helical organization of the PEO chains in the presence of a salting-out solute. The peculiar low transition enthalpy of PEO reflects a low cooperativity of the system thus justifying marginal stability of the helices.
90
V.Y. Grinberg et al. / Polymer 73 (2015) 86e90
Acknowledgment The study was performed at A.N. Nesmeyanov Institute of Organoelement compounds of the Russian Academy of Sciences supported by a grant No. 14-13-00544 from the Russian Science Foundation. References [1] D.M. Back, R.L. Schmitt, Ethylene oxide polymers, in: Encyclopedia of Polymer Science and Technology, vol. 9, John Wiley, New Jersey, 2003, pp. 805e827. [2] S. Saeki, N. Kywahara, M. Nakata, M. Kaneko, Polymer 17 (8) (1976) 685e689. [3] Y.C. Bae, S.M. Lambert, D.S. Soane, J.M. Prausnitz, Macromolecules 24 (15) (1991) 4403e4407. [4] A. Matsuyama, F. Tanaka, Phys. Rev. Lett. 65 (3) (1990) 341e344. [5] S. Bekiranov, R. Bruinsma, P. Pincus, Phys. Rev. E 55 (1) (1997) 577e585. [6] E.E. Dormidontova, Macromolecules 35 (3) (2002) 987e1001. [7] R. Kjellander, E. Florin, J. Chem. Soc. Faraday Trans. 1 77 (1981) 2053e2077. €m, J. Phys. Chem. 89 (23) (1985) 4962e4964. [8] G. Karlstro [9] H. Matsuura, K. Fukuhara, J. Mol. Struct. 126 (JAN) (1985) 251e260. [10] N.B. Graham, M. Zulfiqar, N.E. Nwachuku, A. Rashid, Polymer 30 (3) (1989) 528e533. [11] D. Eagland, N.J. Crowther, C.J. Butler, Polymer 34 (13) (1993) 2804e2808. [12] K. Tasaki, J. Am. Chem. Soc. 118 (35) (1996) 8459e8469. [13] P.L. Privalov, S.A. Potekhin, Methods Enzymol. 131 (1986) 4e51. [14] G.I. Makhatadze, P.L. Privalov, J. Mol. Biol. 213 (2) (1990) 375e384. [15] R.S. Spolar, J.R. Livingstone, M.T. Record, Biochemistry 31 (16) (1992) 3947e3955. [16] E. Freire, Methods Enzymol. 240 (1994) 502e530. [17] E.A. Boucher, P.M. Hines, J. Polym. Sci. Phys. 14 (12) (1976) 2241e2251. [18] Spinger Materials e The Landolt-Bornstein Database; http://www. springermaterials.com/docs/index.html (11-11-2014). [19] H. Durchschlag, P. Zipper, Prog. Coll. Pol. Sci. 94 (1994) 20e39. [20] K. Takahashi, J.M. Sturtevant, Biochemistry 20 (21) (1981) 6185e6190.
[21] P.L. Privalov, Adv. Protein Chem. 33 (1979) 167e241. [22] I. Prigogine, R. Defay, Chemical Thermodynamics, Longmans Green Co, London-N.Y.-Toronto, 1954. [23] W. Pfeil, Protein Stability and Folding. A Collection of Thermodynamic Data, Springer-Verlag, Berlin, Heidelberg, New-York, 1998. [24] G.I. Makhatadze, P.L. Privalov, Adv. Protein Chem. 47 (1995) 307e425. [25] A.S. Dubovik, E.E. Makhaeva, V.Y. Grinberg, A.R. Khokhlov, Macromol. Chem. Phys. 206 (9) (2005) 915e928. [26] A.S. Dubovik, N.V. Grinberg, V.Y. Grinberg, Polym. Sci. Ser. A 52 (6) (2010) 565e573. [27] Y. Okada, F. Tanaka, Macromolecules 38 (10) (2005) 4465e4471. [28] V. Aseyev, H. Tenhu, F.M. Winnik, Adv. Polym. Sci. 242 (2011) 29e89. [29] T. Miyazawa, K. Fukushima, Y. Ideguchi, J. Chem. Phys. 37 (12) (1962) 2764e2776. [30] H. Tadokoro, Y. Chatani, T. Yoshihara, S. Tahara, S. Murahashi, Makromol. Chem. 73 (1) (1964) 109e127. [31] P.G. Assarsson, P.S. Leung, G.J. Safford, Am. Chem. Soc. Div. Polym. Chem. 10 (1969) 1241e1247, 2 Papers for New York meeting. [32] K.J. Liu, J.L. Parsons, Macromolecules 2 (5) (1969) 529e533. [33] J.L. Koeng, A.C. Angood, J. Polym. Sci. A2 8 (10) (1970) 1787e1796. [34] M.L. Alessi, A.I. Norman, S.E. Knowlton, D.L. Ho, S.C. Greer, Macromolecules 38 (22) (2005) 9333e9340. [35] A.I. Norman, Y. Fei, D.L. Ho, S.C. Greer, Macromolecules 40 (7) (2007) 2559e2567. [36] E.A. Bekturov, L.A. Bimendina, Adv. Polym. Sci. 41 (1981), 99e147. [37] R. Zangi, M. Hagen, B.J. Berne, J. Am. Chem. Soc. 129 (15) (2007) 4678e4686. [38] Y.J. Zhang, P.S. Cremer, Curr. Opin. Chem. Biol. 10 (6) (2006) 658e663. [39] R.L. Baldwin, Biophys. J. 71 (4) (1996) 2056e2063. [40] P. Thiyagarajan, D.J. Chaiko, R.P. Hjelm, Macromolecules 28 (23) (1995) 7730e7736. [41] G.B. Fields, D.O.V. Alonso, D. Stigter, K.A. Dill, J. Phys. Chem. 96 (10) (1992) 3974e3981. [42] E.Y. Chi, S. Krishnan, T.W. Randolph, J.F. Carpenter, Pharm. Res. 20 (9) (2003) 1325e1336. [43] M. Petukhov, G. Rychkov, L. Firsov, L. Serrano, Protein Sci. 13 (8) (2004) 2120e2129.
Contents lists available at ScienceDirect
Polymer journal homepage: www.elsevier.com/locate/polymer
Energetics of LCST transition of poly(ethylene oxide) in aqueous solutions Valerij Y. Grinberg a, *, Tatiana V. Burova a, Natalia V. Grinberg a, Alexander S. Dubovik b, Vladimir S. Papkov a, Alexei R. Khokhlov a a b
A.N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Vavilov St. 28, 119991 Moscow, Russian Federation N.M. Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, Kosygin St. 4, 119991 Moscow, Russian Federation
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 April 2015 Received in revised form 22 June 2015 Accepted 20 July 2015 Available online 22 July 2015
Poly(ethylene oxide), PEO, is known to undergo a phase separation transition in aqueous solutions upon heating. This LCST transition is first investigated by high-sensitivity differential scanning calorimetry. Dependences of the transition temperature (Tt), enthalpy (Dth) and heat capacity increment (Dtcp) on the polymer concentration are determined. The transition temperature and enthalpy of PEO decreased with increasing the polymer concentration and followed the Kirchhoff law. A substantial positive value of the transition heat capacity increment of PEO is detected suggesting that the transition is accompanied by an exposure of the polymer hydrophobic groups to water. Comparison of Dtcp with the corresponding change in the accessible surface area of PEO reveals that the LCST transition of PEO may involve cooperative conformational changes of the type of helixecoil transition in PEO macromolecules. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Poly(ethylene oxide) LSCT DSC
1. Introduction Poly(ethylene oxide), PEO, is known as one of the most important water-soluble polymers that has wide practical application [1]. PEO is unlimitedly soluble in water at normal conditions. However, solubility of PEO decreases upon heating, and its aqueous solutions undergo phase separation at a high enough temperature. LCST of aqueous solutions of PEO varies from 100 to 180 C depending on the polymer molecular weight [2,3]. Most of the theories of the phase separation of aqueous PEO solutions [4e6] consider macromolecules of PEO as flexible chains. At the same time, numerous indirect data are available suggesting that macromolecules of PEO in aqueous solution have a helical structure under normal conditions [7e12]. This feature is taken into account in the theory of the LCST behavior of PEO proposed by €m [8]. According to this theory, stability of the helical Karlstro conformation of PEO should depend on temperature. The helix is stable at rather low temperatures, while at elevated temperatures PEO undergoes conformational changes of the type of helixecoil transition. This very transition induces phase separation of the aqueous PEO solutions upon heating. This interesting concept has
* Corresponding author. E-mail address: [email protected] (V.Y. Grinberg). http://dx.doi.org/10.1016/j.polymer.2015.07.032 0032-3861/© 2015 Elsevier Ltd. All rights reserved.
not found a reliable experimental support until now. In this paper we report an experimental evidence of a helixecoil transition of PEO in aqueous solutions associated with the phase separation of these solutions upon heating. The data were obtained by highsensitivity differential scanning calorimetry (HS-DSC) [13]. Besides temperature and enthalpy of the phase separation these data include estimations of change in the partial heat capacity of the polymer related to the phase separation, i.e. the transition heat capacity increment, Dtcp. This parameter correlates with changes in the accessible surface area of a macromolecule (ASA) [14e16]. According to our data the transition heat capacity increment of PEO is positive. This suggests that PEO macromolecules in the initial state (low temperatures) have a hydrophobic interior. One of the probable structures possessing hydrophobic interior might be a helix. Therefore the phase separation of the PEO solutions may be coupled with a conformational helixecoil transition of this polymer. 2. Experimental Poly(ethylene oxide) of a molecular weight of Mh ¼ (43 ± 2) 103 was purchased from Merck and used without additional purification. Aqueous salt-free solutions of this polymer of rather low concentrations revealed phase separation at temperatures 110e130 С. In this temperature range it is not possible to
V.Y. Grinberg et al. / Polymer 73 (2015) 86e90
perform precise calorimetric measurements of the polymer partial heat capacity in an aqueous medium. The most appropriate temperature interval for such measurements is 20e80 С. For this reason we had to reduce the transition temperature of the PEO phase separation to the optimal value (~40 C), lying in the middle of this range. The decrease in the phase separation temperature means a decrease in solvent quality with respect to the polymer. One of the most evident manifestation of the worsening of solvent quality is a decrease in the q-temperature. Boucher and Hines [17] determined values of the q-temperature of PEO in aqueous solutions of various lyotropic salts. They found that the lyotropic salts reduce the q-temperature of PEO. This effect correlates with the salt position in the Hofmeister series. The most distinct changes were observed in case of carbonates and sulfates. Sulfates, being highly thermostable, looked more appropriate for the DSC experiments. The q-temperature of PEO decreases to 41 С at the concentration of ammonium sulfate of 0.5 mol L1. For this reason we have chosen 0.5 М (NH4)2SO4 as a solvent. The PEO concentration was varied from 4 to 75 mg mL1. Calorimetric measurements were carried out with a differential adiabatic scanning microcalorimeter DASM-4 (“Biopribor”, Pushchino, Russia) within the temperature interval 20e70 C at a heating rate of 1.0 K min1. The conversion of raw data to the temperature dependences of the partial heat capacity of the polymer was performed by a standard method [13] using the tabulated values of density and heat capacity of 0.5 M (NH4)2SO4 [18] and the partial specific volume of PEO (v ¼ 0.838 cm3 g1) [19]. The conversion of the temperature dependences of the partial heat capacity to the excess heat capacity functions was carried out by the Takahashi-Sturtevant method [20]. The transition temperature Tt was determined as a temperature that corresponds to the maximum of the excess heat capacity curve, and the transition enthalpy Dth e as an area under this curve. The transition heat capacity increment Dtcp was determined by a counter extrapolation of the linear segments of the partial heat capacity function before and after the transition to the transition temperature. All calculations were performed with the use of a proprietary software NAIRTA 2 (Institute of Biochemical Physics, Moscow) based on the standard algorithms of HS-DSC data processing [13]. The cloud point temperatures Tcp of the PEO solutions of different concentrations were visually determined with an accuracy of ±0.25 С during heating with a constant rate of 1.0 K min1.
87
to determine only the transition temperature because of experimental limitations (a small instrument response at low polymer concentrations and an uncompensated imbalance of the calorimetric cells at high ones). The concentration dependences of the calorimetric transition parameters (Tt, Dth, Dtcp) and of the cloud points are given in Fig. 2. One can see that the calorimetric transition temperatures coincide well with the cloud point temperatures. In the concentration range 18e50 mg mL1, where the precise determination of all calorimetric parameters was possible, the transition temperature and enthalpy decrease from 56.4 to 48.9 С and from 4.2 to 2.4 J g1, respectively, while the transition heat capacity increment remains practically unchanged (Dtcp ¼ 0.31 ± 0.04 J g1 К1). Additionally, for more consistent determination of Dtcp we used the approach based on correlation between the transition enthalpy and temperature [21]. The enthalpy of the PEO phase transition is plotted against the transition temperature in Fig. 3. We observe a good linear correlation between values of these parameters. The correlation implies that heat effects, which are not related to the transition, do not contribute to the calorimetric enthalpy. In this case the calorimetric parameters satisfy the Kirchhoff law [22], which assigns the slope of the linear dependence Dth(Tt) to the transition heat capacity increment Dtcp. Applying the Kirchhoff law to the data in Fig. 3, we determine Dtcp ¼ 0.22 ± 0.02 J g1 К1. This is close to the result of the direct calorimetric determination of the transition heat capacity increment, as described above (Dtcp ¼ 0.31 ± 0.04 J g1 К1). The agreement of the direct and indirect determinations of the heat capacity increment suggests the thermodynamic consistency of the average value of this parameter Dtcp ¼ 0.27 ± 0.05 J g1 К1. It is necessary to emphasize that this parameter is positive and similar by the magnitude to unfolding heat capacity increments of proteins [23]. It is well recognized that the positive heat capacity increment of protein unfolding is a clear manifestation of existence of hydrophobic core in protein molecule [24]. Here we come to two important differences between PEO and the most studied thermoresponsive polymers, poly(Nisopropylacrylamide) (PNIPAM) and poly(N-vinylcaprolactam) (PVCL). For these two polymers the enthalpy of LCST transition is of about 60 J g1 and the transition heat capacity increment is negative (~0.6 J g1 K1) [25,26].
3. Results and discussion Fig. 1 shows an example of the temperature dependence of the partial heat capacity of PEO in aqueous solution at the polymer concentration of 22.5 mg mL1. The partial heat capacity increases linearly with increasing temperature within the interval from 20 to 50 C, then passes though a sharp maximum and reaches a constant level notably exceeding the partial heat capacity of the polymer in the pre-transition area. The temperature of the partial heat capacity maximum coincides with the cloud point temperature of the PEO solution. This allows us to assign the observed changes in heat capacity in the post-transition area to the phase separation of the system. It is important that the phase separation of the PEO aqueous solutions is accompanied by an increase in the polymer partial heat capacity (Dtcp > 0) along with a trivial heat absorbance (Dth > 0). Similar temperature dependences of the partial heat capacity of PEO were determined at different polymer concentrations from 4 to 75 mg mL1. However, their complete quantitative analysis (that is, determination of all calorimetric parameters: Tt, Dth and Dtcp) was only possible within the more narrow interval from 18 to 50 mg mL1. At the lower and higher concentrations we were able
Fig. 1. Partial heat capacity of PEO in aqueous solution (polymer concentration 22.5 mg mL1, 0.5 M (NH4)2SO4). The thin and dash lines represent a transition base line and a linear approximation of the pre-transition segment of the partial heat capacity function, respectively.
88
V.Y. Grinberg et al. / Polymer 73 (2015) 86e90
It is possible to relate the difference in the transition enthalpies of PEO and the poly(N-alkylamides) with differences in hydration mechanisms of these types of polymers. The hydration mechanism of PEO is associated with binding of water molecules to independent identical sites on the polymer matrix [4]. On the contrary, the poly(N-alkylamides) hydration seems to be very cooperative [27]. Heat effects of phase separation of aqueous solutions of thermoresponsive polymers is commonly attributed to their dehydration [28]. The non-cooperative hydration mechanism assumes that the dehydration constitutes dissociation of bonds between water molecules and the polymer matrix. On the other hand, in the case of the cooperative mechanism the dehydration should additionally include breakdown of bonds between water molecules bound to neighboring sites on the polymer matrix. That is why the transition enthalpy of the poly(N-alkylamides) greatly exceeds the transition
enthalpy of PEO. The phase separation of aqueous solutions of the poly(Nalkylamides) is accompanied by a decrease in the partial heat capacity of the polymer (Dtcp < 0) [25,26]. It is due to the fact that some links of the polymer chain, initially accessible to water molecules, become inaccessible to them after the phase transition. This indicates existence of a hydrophobic core in the concentrated polymer phase formed as a result of the phase separation. A positive value of the transition heat capacity increment of PEO suggests that some part of hydrophobic fragments of PEO macromolecule in its initial conformation at low temperatures is inaccessible to water molecules [14,16]. The question arises what structure of PEO may have a hydrophobic interior? The chain stereochemistry of PEO allows the formation of helical conformation [29]. This conformation is experimentally observed in the crystal state of the polymer [30]. The data on the probability of existence of PEO helixes in aqueous solution are rather contradictory. On the one hand, there are indirect experimental data [9e11,31e33] and certain model simulations [7,8,12] suggesting that molecules of PEO retain helical conformation in aqueous medium. On the other hand, the SANS data show that molecules of PEO in aqueous solution have the conformation of a random coil [34]. The reason for this contradiction is probably a high lability of the PEO conformation in aqueous solution. In order to shift the conformational equilibrium towards the helix it is necessary to increase its stability with respect to the coil conformation. This can be achieved in two ways e either by strengthening bonds between peripheral oxygen atoms, or by enhancing interaction of hydrophobic groups forming the helix interior. The first scenario was described in the works of Alessi et al. [34] and Norman et al. [35]. It has been shown by SANS that the helix is a preferential conformation of PEO in solutions of neat carboxylic acids with a number of carbon atoms from 3 to 5. The nature of such a phenomenon could be explained in the following manner. It is well known that oxygen atom of PEO can form H-bond with the protonated carboxylic group. This interaction determines the ability of PEO to form complexes with polymeric acids in the protonated state [36]. One can imagine that the carboxylic acids, being bound to the neighboring oxygen atoms on the helix surface, create bonds between the helix turns by means of van der Waals
Fig. 2. Transition temperature (a), enthalpy (b) and heat capacity increment (c) of PEO in aqueous solutions (0.5 M (NH4)2SO4) vs the polymer concentration: (1) e calorimetric data; (2) e cloud points (explanations in text).
Fig. 3. Correlation between the transition enthalpy and temperature for PEO in aqueous solutions (0.5 M (NH4)2SO4) of different polymer concentrations according to the Kirchhoff law. The slope of correlation line is 0.22 ± 0.02 J g1 K1.
V.Y. Grinberg et al. / Polymer 73 (2015) 86e90
interactions of their alkyl groups. The second scenario of the PEO helix stabilization implies the strengthening of hydrophobic interaction of the groups, forming interior of the helix. This situation seems to be relevant to the conditions used in our study. It is well known that lyotropic salts, such as ammonium sulfate, enhance hydrophobic interaction in aqueous medium [37] as evidenced by multiple effects, such as a decrease in the precipitation temperature of amphiphilic polymers [38] or an increase in conformational stability of globular proteins and helical peptides in solutions of lyotropic salts [39]. Thiyagarajan et al. [40] have shown by means of SANS that in solutions of sodium carbonate, which is a strong salting-out solute, PEO is represented by rod-like particles of the length proportional to the polymer molecular weight, determined in neat water. From these data it can be concluded that the length of such a particle per one polymer link is equal to 3.0 ± 0.1 Å. On the other hand, the results of molecular modeling [12] show that the helix length per one link is of about 2.9 Å. This coincidence may be considered as an indirect confirmation of the concept that PEO adopts the helical conformation in solutions of lyotropic salts. On this basis it is reasonable to suggest that under the conditions of our experiment, i.e. in 0.5 M solution of ammonium sulfate, the helical conformation of PEO is rather stable at temperatures below the phase separation temperature. Upon heating the helices melt, their hydrophobic interior breaks, the chain hydrophobic groups become exposed to the aqueous surrounding, their random association begins and causes the polymer precipitation. In certain aspects this resembles the denaturation behavior of globular proteins, which demonstrate similar disintegration of a molecular hydrophobic core upon heating that often leads to the precipitation of the denatured proteins [41,42]. It has been shown on the example of proteins that the transition heat capacity increment is closely related to the change in the accessible surface area (DtASA) of a macromolecule associated with the transition [15,16,24]. According to the data by Spolar et al. [15], hydration of apolar and polar groups is accompanied by the intrinsic changes in heat capacity. Values of these changes per unit of the accessible surface area equal to Dh CpAPO ¼ 1.338 J mol1 К1 Å2 and Dh CpPOL ¼e 0.585 J mol1 К1 Å2, respectively. The universality of these increments was shown for a great number of compounds. Taking into account this fact, we can assume that the heat capacity increment of the PEO transition is directly related to the change in the chain hydration as a result of the helix unwinding. If so, the specific heat capacity increment can be calculated as:
. M0 Dt cp ¼ Dh CpAPO Dt ASAAPO þ Dh CpPOL Dt ASAPOL
(1)
where DtASAAPO and DtASAPOL are the changes in the accessible area of the hydrophobic and hydrophilic surface of PEO monomer unit induced by the helixecoil transition, respectively; and M0 ¼ 44 g mol1 is the molecular weight of PEO monomer unit. According to the molecular modeling data [12], the PEO helix in water has the following characteristics: the helix pitch LH ¼ 16 Å; the diameter of the helix DH x 5 Å; the number of monomers per a helix turn nH ¼ 11/2. Accordingly, the area of the accessible surface of the helix per monomer is:
ASAH ¼
pLH DH nH
(2)
A value of the accessible surface area per monomer for PEO in the coil state can be determined by an additive scheme [14]:
ASAC ¼ 2ASACH2 þ ASAO
(3)
where ASACH2 and ASAO are the accessible surface areas of the CH2
89
group and an oxygen atom, respectively. The value ASACH2 may be also estimated by the additive scheme, using values of the accessible surface area of the leucine and valine residues [14] ASAILE ¼ 137 Å2 and ASAVAL ¼ 117 Å2: ASACH2 ¼ ASAILE ASAVAL . A value of the accessible surface area of the oxygen atom ASAO ¼ 50 Å2 is reported in the work by Petukhov et al. [43]. It is important that in the first approximation the distribution of the accessible area of the PEO monomer by hydropathy is the same for the coil and helix. It can be roughly estimated by the fractions of the hydrophobic and hydrophilic surfaces XAPO ¼ 2ASACH2 =ASAC ¼ 0:444 and XPOL ¼ ASAO/ASAC ¼ 0.556. Thus the transition change in hydrophobic and hydrophilic accessible surface area of PEO per monomer will be:
Dt ASAPOL ¼ XPOL ðASAC ASAH Þ
(4)
and
Dt ASAAPO ¼ XAPO ðASAC ASAH Þ
(5)
According to the calculations by Equations (1)e(5), the heat capacity increment of the helixecoil transition of PEO in aqueous solution is equal to 0.27 J g1 К1. This estimate coincides with the average value of the specific transition heat capacity increment of PEO determined directly from the HS-DSC data and by the Kirchhoff law (Dtcp ¼ 0.27 ± 0.05 J g1 К1) . Thus, the calorimetric data on energetics of the phase separation of aqueous solutions of PEO point to at least two particular features of behavior of this polymer in aqueous salt solution, which may be important for structural considerations. First, a relatively small enthalpy of the PEO phase transition (about of several Joule per gram of the polymer) reflects presumably a noncooperative mechanism of the polymer hydration. Second, the transition is accompanied by increase in the partial heat capacity of the polymer typical for protein unfolding when initially buried hydrophobic groups of the protein become accessible to water molecules. On this basis we could suggest that macromolecules of PEO in the pre-transition state assume a conformation with a defined hydrophobic core. Such a conformation could be helix, existence of which was shown to be consistent with numerous indirect experimental data and some results of molecular simulations. Upon heating the helix melts providing complete accessibility of PEO links to water molecules that provokes the phase separation.
4. Conclusion Despite a long-term representative history of investigation of PEO, its solution structure remains an open question. Many reliable facts indicate a clear tendency of PEO to form rod-like particles in aqueous solutions, particularly under salting-out conditions. Fine characterization of these structures is obviously complicated by their high lability and sensitivity to various polymer and environment parameters, such as salt nature and concentration, temperature, molecular characteristics of PEO, etc. The experimental and theoretical approaches that include consideration of the transition energetics may help to fill the structural gap, exploring phase and conformational transitions of these labile structures and analyzing contributions of certain interactions to the transition parameters. The first direct data on energetics of the phase separation of aqueous solutions of PEO support the existing hypothesis on the probability of helical organization of the PEO chains in the presence of a salting-out solute. The peculiar low transition enthalpy of PEO reflects a low cooperativity of the system thus justifying marginal stability of the helices.
90
V.Y. Grinberg et al. / Polymer 73 (2015) 86e90
Acknowledgment The study was performed at A.N. Nesmeyanov Institute of Organoelement compounds of the Russian Academy of Sciences supported by a grant No. 14-13-00544 from the Russian Science Foundation. References [1] D.M. Back, R.L. Schmitt, Ethylene oxide polymers, in: Encyclopedia of Polymer Science and Technology, vol. 9, John Wiley, New Jersey, 2003, pp. 805e827. [2] S. Saeki, N. Kywahara, M. Nakata, M. Kaneko, Polymer 17 (8) (1976) 685e689. [3] Y.C. Bae, S.M. Lambert, D.S. Soane, J.M. Prausnitz, Macromolecules 24 (15) (1991) 4403e4407. [4] A. Matsuyama, F. Tanaka, Phys. Rev. Lett. 65 (3) (1990) 341e344. [5] S. Bekiranov, R. Bruinsma, P. Pincus, Phys. Rev. E 55 (1) (1997) 577e585. [6] E.E. Dormidontova, Macromolecules 35 (3) (2002) 987e1001. [7] R. Kjellander, E. Florin, J. Chem. Soc. Faraday Trans. 1 77 (1981) 2053e2077. €m, J. Phys. Chem. 89 (23) (1985) 4962e4964. [8] G. Karlstro [9] H. Matsuura, K. Fukuhara, J. Mol. Struct. 126 (JAN) (1985) 251e260. [10] N.B. Graham, M. Zulfiqar, N.E. Nwachuku, A. Rashid, Polymer 30 (3) (1989) 528e533. [11] D. Eagland, N.J. Crowther, C.J. Butler, Polymer 34 (13) (1993) 2804e2808. [12] K. Tasaki, J. Am. Chem. Soc. 118 (35) (1996) 8459e8469. [13] P.L. Privalov, S.A. Potekhin, Methods Enzymol. 131 (1986) 4e51. [14] G.I. Makhatadze, P.L. Privalov, J. Mol. Biol. 213 (2) (1990) 375e384. [15] R.S. Spolar, J.R. Livingstone, M.T. Record, Biochemistry 31 (16) (1992) 3947e3955. [16] E. Freire, Methods Enzymol. 240 (1994) 502e530. [17] E.A. Boucher, P.M. Hines, J. Polym. Sci. Phys. 14 (12) (1976) 2241e2251. [18] Spinger Materials e The Landolt-Bornstein Database; http://www. springermaterials.com/docs/index.html (11-11-2014). [19] H. Durchschlag, P. Zipper, Prog. Coll. Pol. Sci. 94 (1994) 20e39. [20] K. Takahashi, J.M. Sturtevant, Biochemistry 20 (21) (1981) 6185e6190.
[21] P.L. Privalov, Adv. Protein Chem. 33 (1979) 167e241. [22] I. Prigogine, R. Defay, Chemical Thermodynamics, Longmans Green Co, London-N.Y.-Toronto, 1954. [23] W. Pfeil, Protein Stability and Folding. A Collection of Thermodynamic Data, Springer-Verlag, Berlin, Heidelberg, New-York, 1998. [24] G.I. Makhatadze, P.L. Privalov, Adv. Protein Chem. 47 (1995) 307e425. [25] A.S. Dubovik, E.E. Makhaeva, V.Y. Grinberg, A.R. Khokhlov, Macromol. Chem. Phys. 206 (9) (2005) 915e928. [26] A.S. Dubovik, N.V. Grinberg, V.Y. Grinberg, Polym. Sci. Ser. A 52 (6) (2010) 565e573. [27] Y. Okada, F. Tanaka, Macromolecules 38 (10) (2005) 4465e4471. [28] V. Aseyev, H. Tenhu, F.M. Winnik, Adv. Polym. Sci. 242 (2011) 29e89. [29] T. Miyazawa, K. Fukushima, Y. Ideguchi, J. Chem. Phys. 37 (12) (1962) 2764e2776. [30] H. Tadokoro, Y. Chatani, T. Yoshihara, S. Tahara, S. Murahashi, Makromol. Chem. 73 (1) (1964) 109e127. [31] P.G. Assarsson, P.S. Leung, G.J. Safford, Am. Chem. Soc. Div. Polym. Chem. 10 (1969) 1241e1247, 2 Papers for New York meeting. [32] K.J. Liu, J.L. Parsons, Macromolecules 2 (5) (1969) 529e533. [33] J.L. Koeng, A.C. Angood, J. Polym. Sci. A2 8 (10) (1970) 1787e1796. [34] M.L. Alessi, A.I. Norman, S.E. Knowlton, D.L. Ho, S.C. Greer, Macromolecules 38 (22) (2005) 9333e9340. [35] A.I. Norman, Y. Fei, D.L. Ho, S.C. Greer, Macromolecules 40 (7) (2007) 2559e2567. [36] E.A. Bekturov, L.A. Bimendina, Adv. Polym. Sci. 41 (1981), 99e147. [37] R. Zangi, M. Hagen, B.J. Berne, J. Am. Chem. Soc. 129 (15) (2007) 4678e4686. [38] Y.J. Zhang, P.S. Cremer, Curr. Opin. Chem. Biol. 10 (6) (2006) 658e663. [39] R.L. Baldwin, Biophys. J. 71 (4) (1996) 2056e2063. [40] P. Thiyagarajan, D.J. Chaiko, R.P. Hjelm, Macromolecules 28 (23) (1995) 7730e7736. [41] G.B. Fields, D.O.V. Alonso, D. Stigter, K.A. Dill, J. Phys. Chem. 96 (10) (1992) 3974e3981. [42] E.Y. Chi, S. Krishnan, T.W. Randolph, J.F. Carpenter, Pharm. Res. 20 (9) (2003) 1325e1336. [43] M. Petukhov, G. Rychkov, L. Firsov, L. Serrano, Protein Sci. 13 (8) (2004) 2120e2129.